Population: In a city of 40,000 people, there are 15,000 people under 25 years of age. What percent of the
1 answer:
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<u>Red</u>
This is a circle with center (h, k) at (0,0) and radius (r) = 6
Formula: (x - h)² + (y - k)² = r²
Answer: x² + y² = 36
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<u>Blue</u>
This is a circle with center (h, k) at (2,2) and radius (r) = 1
Formula: (x - h)² + (y - k)² = r²
Answer: (x - 2)² + (y - 2)² = 1
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<u>Green:</u>
This is a circle with center (h, k) at (-2,-2) and radius (r) = 1
Formula: (x - h)² + (y - k)² = r²
Answer: (x + 2)² + (y + 2)² = 1
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<u>Purple:</u>
This is an ellipse with center (h, k) at (0,-2) and radius on the x-axis (a) = 3 and radius on the x-axis (b) = 1
Formula:
Answer:
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<u>Black:</u>
This is a parabola with vertex (h, k) at (0,-6) and vertical stretch (a) = -1
Formula: y = a(x - h)² + k
Answer: y = -x² - 6
Step-by-step explanation:
The upstream speed is S / t₁, and the downstream speed is S / t₂.
If we say f is the speed of the fish in calm water, and r is the speed of the river, then:
f − r = S / t₁
f + r = S / t₂
If we say T is the time it takes to cross the river, then the speed perpendicular to the river is ℓ/T, the speed parallel to the river is r, and the overall speed is f.
Using Pythagorean theorem:
f² = (ℓ/T)² + r²
f² − r² = (ℓ/T)²
(f − r) (f + r) = (ℓ/T)²
(S / t₁) (S / t₂) = (ℓ/T)²
S² / (t₁ t₂) = (ℓ/T)²
(t₁ t₂) / S² = (T/ℓ)²
√(t₁ t₂) / S = T/ℓ
T = ℓ√(t₁ t₂) / S
